Superconvergence of discontinuous Galerkin methods for two-dimensional hyperbolic equations
Document Type
Article
Publication Date
1-1-2015
Abstract
© 2015 Society for Industrial and Applied Mathematics. This paper is concerned with superconvergence properties of discontinuous Galerkin (DG) methods for two-dimensional linear hyperbolic conservation laws over rectangular meshes when upwind fluxes are used. We prove, under some suitable initial and boundary discretizations, the (2k + 1)th order superconvergence rate of the DG approximation at the downwind points and for the cell averages, when piecewise tensor-product polynomials of degree k are used. Moreover, we prove that the gradient of the DG solution is superconvergent with a rate of (k + 1)th order at all interior left Radau points; and the function value approximation is superconvergent at all right Radau points with a rate of (k + 2)th order. Numerical experiments indicate that the aforementioned superconvergence rates are sharp.
Publication Title
SIAM Journal on Numerical Analysis
Recommended Citation
Cao, W.,
Shu, C.,
Yang, Y.,
&
Zhang, Z.
(2015).
Superconvergence of discontinuous Galerkin methods for two-dimensional hyperbolic equations.
SIAM Journal on Numerical Analysis,
53(4), 1651-1671.
http://doi.org/10.1137/140996203
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/12334
